The complete weight enumerator of the Reed-Solomon code with dimension two or three

12/28/2021
by   Canze Zhu, et al.
0

It is well-known that Reed-Solomon codes and extended Reed-Solomon codes are two special classes of MDS codes with wide applications in practice. The complete weight enumerators of these codes are very important for determining the capability of both error-detection and error-correction. In this paper, for any positive integer m and prime p, basing on the character sums, we determine the complete weight enumerators of the Reed-Solomon code and the extended Reed-Solomon code with dimension k (k=2,3) over 𝔽_p^m, explictly, which are generalizations of the corresponding results in <cit.>.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
07/06/2021

Complete weight enumerators for several classes of two-weight and three-weight linear codes

In this paper, for an odd prime p, by extending Li et al.'s construction...
research
12/11/2021

The construction for several few-weight linear codes and their applications

In this paper, for any odd prime p and an integer m≥ 3, several classes ...
research
04/25/2022

The equivalence of GRS codes and EGRS codes

Generalized Reed-Solomon and extended generalized Reed-Solomon (abbrevia...
research
08/18/2022

Near-MDS Codes from Maximal Arcs in PG(2,q)

The singleton defect of an [n,k,d] linear code C is defined as s( C)=n-k...
research
12/09/2020

Complete weight enumerators of a class of linear codes with four or five weights

In this paper, based on the theory of defining sets, a class of four-wei...
research
08/31/2022

When Variable-Length Codes Meet the Field of Error Detection

Given a finite alphabet A and a binary relation τ⊆ A^*× A^*, a set X is ...
research
12/11/2020

Subfield codes of linear codes from perfect nonlinear functions and their duals

Let 𝔽_p^m be a finite field with p^m elements, where p is an odd prime a...

Please sign up or login with your details

Forgot password? Click here to reset